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DIPS year-to-year correlations, 1972-1992 (August 5, 2003)
Discussion ThreadPosted 12:04 a.m.,
August 20, 2003
(#142) -
Matt Goff
Posted 10:32 a.m., August 19, 2003 (#132) - Arvin Hsu
I think it comes down to why we're adding variances:
In a normal distribution, you add when you add two random variables.
eg. X ~ Norm(3,.05^2), Y ~ Norm(4,.03^2)
Z = X+Y
Z ~ (7,.05^2+.03^2)
Although I'm not yet convinced it works this way for a normal p affecting a binomial, the sims seem to bear it out. Why? Well it makes sense. On some level, you're adding two r.v.'s, the binomial
and the normal.
...
I have not had the time to figure out everything that has been talked about so hopefully this comment is relevant:
It seems to me that your concern about the addition of variances may be alleviated by recalling that a binomial is approximately normal for large n (thanks to the good old Central Limit Theorem). I can't remember the exact rule of thumb, but it seems like n*p>25 or something like that. In any case, if I understand what I have been reading, the n should be quite adequate for the normal approximation to hold.